There's a story often told about Lauren Cuthbertson that when she danced her first Juliet, aged 19, she went on with the mother of all hangovers. So is it true? "It was just a joke!" she insists, eyes widening. "Five minutes before the start of the show, everyone around me was being really tense. Another dancer was feeling sick, and I just said, for a laugh, 'Are you hungover? God, so am I.'"

Cuthbertson clicks her tongue reprovingly at her younger, wilder self, though when she mimes the brief but stricken panic she induced in her boss, Monica Mason, it's anything but repentant and very funny. The fact the story has stuck says a lot about Cuthbertson's reputation as the least grand, the least diva-like of ballerinas. On stage, she might be praised as an extraordinary actor, as intelligent musically as she is stylistically; she might be muse to Wayne McGregor and Christopher Wheeldon; she might be on the verge of making her debut as Manon, one of the most challenging roles in the Royal Ballet's repertory. But to her colleagues, she is simply known as Lozza, Chicken or (to her friend and fellow dancer Edward Watson) Loopy Fucking Loo. Off stage, scrubbed clean of makeup, the 27-year-old doesn't look very different from the skinny, freckled kid from Devon who was taken to ballet classes by her mum in order to burn off her tomboy restlessness.

Cuthbertson's lack of pretension seems to go with the territory for British ballerinas. Darcey Bussell, after all, was loved for her self-deprecating humour as well as for her dancing. And Cuthbertson thinks it's also connected with the fact that so many of the dancers in the Royal Ballet also went to its school. "Lots of us grew up together. We feel part of a group, and it can be hard splitting yourself off from that, especially when you first join the company. You're very young, you want the support of your friends, and you don't want to look as if you're being too pushy. I had huge ambitions, but I was scared to show what I could really do. So at work, I'd be jokey, have a laugh, blend in. Then I'd go home and practise really hard."

Eighteen months of anguish

Despite Cuthbertson's reticence, she was unable to hide her exceptional potential. During her first two seasons in the corps de ballet, she was chosen to understudy a range of solo roles, many of which she got to perform. "There were a lot of injuries, so even though I was brand spanking new I was dancing all the fairies in Sleeping Beauty, Gamzatti [in La Bayadère] and then Juliet."

One role, however, was a challenge too far: the classically finessed lead in Balanchine's Symphony in C. Cuthbertson pulls a goofy face. "In the audience's eyes, a diamond has to come on stage – but I just felt like this kid." Feeling she'd been forced into the role too early, and worried other dancers were overtaking her, Cuthbertson became demoralised. "I felt like I'd hit a plateau. It was awful. I didn't know what I was doing wrong and I was too shy to ask."

For two years, she stalled and that could easily have been where her story ended – among the ranks of soloists who never find their way into the spotlight. However, one of her former teachers noticed she was struggling and suggested, briskly, she should jumpstart her career by setting herself outside challenges. So she had some private coaching and entered Varna, the prestigious international ballet competition held in Bulgaria. It did the trick. Cuthbertson walked away with joint silver and felt a change both in herself and in how others saw her. In 2008, she was promoted to principal.

Then, a few months later Cuthbertson again found herself at a low ebb. She had sprained her foot, and began suffering from inexplicable fatigue. By early 2009, when she was making her debut in Giselle, she was barely able to function. "It was a farce. I was rehearsing in trainers because my foot was still bad. My head was in a complete fog, and I had terrible cramps all round my body."

She was still able to dance a Giselle that was hailed by the Spectator as "the perfect modern day incarnation of the Romantic ideal". But it turned out she was suffering from glandular fever – and there was worse to come. As soon as the symptoms receded, they were replaced by those of postviral fatigue syndrome, or ME. Looking at Cuthbertson now, as she perches cross-legged and laughing on a sofa in the Opera House, it's hard to credit the long months of illness she endured when she was barely able to lift her head off the pillow, only able to increase the exercise she took by increments of one or two minutes per day. "It was a surreal time," she says, "and I did have one breakdown when I just wept and wept to my doctor."

Now she's made a full recovery, Cuthbertson can find some worth in those 18 months of anguish. They taught her the value of patience and structure in her training. They also taught her the idiocy of concealing her ambition. "When I came back to work, I was burning."

It showed. Her return season was nothing short of heroic. She added major ballets such as Cinderella to her repertory, and Wheeldon created the title role in his Alice's Adventures in Wonderland for her. This 2011 work was the first full-length ballet to have been created at the Royal for 16 years, and Cuthbertson was fresh, funny and winningly uncute. Yet, while her recovery tells us everything about her tenacity, what's harder to pin down are the qualities that make her such an exceptional ballerina. Some dancers have a defining attribute: Sylvie Guillem's ear-high extensions, Alina Cojocaru's airy delicacy, Natalia Osipova's enormous jump. But what makes Cuthbertson special is more to do with the quality of her presence. Her performances are very personal: you never see a cliched gesture or a "ballet dancer expression". Even in abstract work, her dancing is peculiarly spontaneous, transparent in its lack of rhetoric or airs.

It's a little awkward to tell a ballerina you think she lacks star quality, yet Cuthbertson is game enough to consider it a compliment. "I may be off the mark," she says, "but when I'm performing, I want the audience to come to me, to my world. Even in the tits-and-teeth ballets, which are all about display, I like to draw people close rather than be too obvious." The same goes for story ballets. Of her forthcoming Manon, she says: "I don't want to come on stage and go, 'This is MY MANON.' I want her character to emerge more slowly."

Cuthbertson prepares intensively for each role, playing the music constantly, even choosing a signature perfume to wear on stage. And she resists the temptation to cherrypick aspects of other dancers' performances to emulate or improve. "If I'm going to be truly confident in a role, I have to go into it naked. I can always sense when something is fake for me, when I'm trying to create an effect. Like the first scene in Manon: at first, it didn't feel true to me, I didn't know what she was thinking. It's only when I know where I'm coming from that a role makes sense and I'm away."

Getting down and dirty

She's learning Manon with Sergei Polunin (touted as the next Nureyev) and together they have to dance some of the most swooningly erotic pas de deux in the repertory. Cuthbertson grins at the memory of being partnered by Polunin in school. "I'd be thinking, 'Is he actually going to get me up there?' But now he's this beast. I love being partnered by him – he carries on dancing even while he's holding you. It's how I'd do it if I was partnering myself."

Cuthbertson reckons she has a good 10 years of dancing left. She's hungry to create more character roles, especially after the experience of Alice. "It was so exciting, building her up from scratch, working out who she was. I felt such a responsibility to everyone who'd dance the role after me. Now I'd like to work on another more grown-up character. I wonder if there's another story out there we could create."

She's also hungry to extract more from the ballets she's already danced. "I hate debuts: you're always worrying about your costume, your hair. I'm impatient to get down and dirty with the choreography. But so far, I've only been able to do a few shows of each role. When I think about it, I could cry. I'm here, I can do it – and I want to do more."

•Lauren Cuthbertson debuts as Manon is at Royal Opera House, London WC2 on 8 November. Box office: 020-7304 4000.